InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `A = 2 tan^(-1) (2 sqrt2 -1) and B = 3 sin^(-1) ((1)/(3)) + sin^(-1) ((3)/(5))`, then which is greater ? |
|
Answer» We have `A = 2 tan^(-1) (2 sqrt2 -1) = 2 tan^(-1) (1.828)` `rArr A gt 2 tan^(-1) sqrt3` `rArr A gt (2pi)/(3)` Now, `sin^(-1) ((1)/(3)) lt sin^(-1) ((1)/(2))` `rArr sin^(-1) ((1)/(3)) lt (pi)/(6)` `rArr 3 sin^(-1).(1)/(3) lt (pi)/(2)` Further, `sin^(-1) ((3)/(5)) = sin^(-1) (0.6) lt sin^(-1) ((sqrt3)/(2))` `rArr sin^(-1) ((3)/(5)) lt (pi)/(3)` `rArr B = 3 sin^(-1) ((1)/(3)) + sin^(-1) ((3)/(5)) lt (pi)/(2) + (pi)/(3)` `rArr B lt (5pi)/(6)` From this, we really cannot relate A and B. Now, `3 sin^(-1) ((1)/(3)) = sin^(-1) [3.(1)/(3) - 4((1)/(3))^(3)]` `= sin^(-1) ((23)/(27))` `= sin^(-1) (0.852)` `rArr 3 sin^(-1) ((1)/(3)) lt sin^(-1) ((sqrt3)/(2)) = (pi)/(3)` Hence, `B = 3 sin^(-1) ((1)/(3)) + sin^(-1) ((3)/(5)) lt (pi)/(3) + (pi)/(3) = (2pi)/(3)` `:. A gt B` |
|